A Study Of Fractional Order PID Control Based On Grey Prediction Control

A single control method can not meet people’s needs, because of the existence of diversity, complexity and uncertainty in practical engineering. Therefore, a large number of control methods combine with various algorithms were presented, such as Fuzzy PID, Neural Network PID, Expert PID and Grey PID.The Grey PID control is a control algorithm using grey control theory to the PID control algorithm. Its behavior model displace mathematical model of a system, meanwhile the prediction error is used to the parameters turning of PID control. The Grey PID control eliminates the limitation of PID control algorithm, and improves the control quality. It is widely used for real-time control with the advantages of less original dates or calculation steps, as well as only two adaptive parameters need to be identified.With the fractional calculus become focus, the researches on fractional order PIλDμ controller also rise. Fractional order PIλDμ controller extends the traditional integer order PID control theory. The range of the whole controller parameter set larger, meanwhile the object can be controlled more flexibly, due to the introduction of integral order λ and differential order μ.According to the theory of grey system and fractional order PIλDμ controller, this paper presents an algorithm of grey fractional order PIλDμ controller. It both has the advantages of grey prediction and fractional order PIλDμ controller. The main research work of this paper can be described as follows:1. It discusses the modeling method of grey model, and the defects of the grey forecasting model. Then some new improved methods are proposed. This paper adopts transformation for the original series to improve the accuracy of the model and to obtain better forecasting results.2. It describes the development and related theory of fractional order PIλDμ controller. Including the definition of fractional calculus, fractional differential equation, the numerical solution and digital description of fractional order controller principle. A simulation experiment is taken to illustrate that the fractional order PIλDμ controller has more advantages compared with the integer one.3. This paper deeply analyzes and investigates the principle of the grey fractional order PIλDμ controller. An integrated error is adopted as the input of fractional order PIλDμ controller, which is combined by the system output error and the system prediction output error. The feasibility and effectiveness are proved by a simulation experiment.